基于模拟退火算法的宽角度X射线超反射镜设计研究

应用于硬X射线波段的宽带多层膜光学元件———宽角度X射线超反射镜的设计可以归结为一个连续变量的多维多极值的全局优化问题。缺少一种有效的全局优化方法是阻碍解决这一难题的一个关键。模拟退火算法是一种简单而且通用的全局优化算法。结合光学多层膜的设计原理提出了利用模拟退火算法来进行宽角度X射线超反射镜设计的新方法。结合已有的方法选择了W和C作为膜层的膜对材料,设计出Cu的Kα线处角度范围0.9°~1.1°反射率达到20%的宽角度X射线超反射镜。并在此基础上采用改进的自适应模拟退火算法实现了Cu的Kα线处宽角度X射线超反射镜的理想设计结果。设计结果表明了模拟退火算法在多层膜最优化设计领域的正确性和有效性。

Wide-Angle X-Ray Supermirror Design Using Simulated Annealing Algorithm

The design of wide angle X-ray supermirror, wide band-pass multilayer optical elements operating in the hard X-ray region is attributed to the global optimization of the multi-dimensional extremum of continuous variables. Lack of powerful optimization method is the key obstacle to this problem. Simulated annealing algorithm is a simple and universal global optimization method. Based on the theory of optical multilayers, a new method of designing wide angle X-ray supermirror using simulated annealing algorithm is presented. The coating materials pair W/C is selected by the combination of the Spiller' and Yamamoto' criterions. The designed supermirror with high and flat reflectivity of 20%, over a grazing incident angle range 0.9°～1.1° at the wavelength of Cu Kα line is completed. Furthermore, the improved adaptive simulated annealing algorithm is used to obtain a better design result. The validity of the proposed algorithm is shown by the example involving multilayer design.